Serious concerns over the legal status of the 3 million EU citizens living in Britain have been fuelled by Theresa May’s confirmation on Sunday that she regards their future as part of Brexit negotiations.

May’s Tory leadership rival Andrea Leadsom issued a rapid riposte, pledging during her campaign launch that their futures should be not “used as bargaining chips” in those negotiations.

The threat that the future in Britain of the 3 million EU nationals might be used “as hostages in the negotiations”, to be traded to safeguard the position of the 1.2 million Britons living in Europe was first made explicit by the former Ukip leader Lord Pearson last Wednesday.

To criticism from all sides, he told the Lords: “Do the government agree however, that if the EU were to get difficult with our nationals living there, it is we who hold the stronger hand if we retaliate, because so many more of them are living here?”

As the immigration lawyer Colin Yeo has pointed out on his Free Movement blog: “Basically Lord Pearson of Rannoch, who speaks for Ukip, basically suggested holding 3 million EU nationals as hostage in negotiations with the EU. It did not go down well with anyone else.”

Anxieties over the future of EU nationals in Britain have been fuelled by reports of street incidents and hate messages in which Poles, among others, have been told that they will soon be sent home. Labour’s Yvette Cooper has said they are already being targeted by racist “go home” and repatriation campaigns.

In the run-up to the referendum, the leave campaign tried to dispel such fears by promising to guarantee the position of EU citizens in Britain by saying those who were lawfully resident in the UK would be offered indefinite leave to remain.

But May has refused to give this guarantee. “We are still a member of the EU – there is no change in their position currently. But of course as part of the negotiation we will need to look at this question of people who are here in the UK from the EU,” she told ITV’s Peston on Sunday show. “I want to ensure that we are able to not just guarantee the positions of those people but guarantee the positions of British citizens in other member states.”

The lack of a guarantee, however, has prompted a highly unusual cross-party consensus. A letter to the Daily Telegraph on Monday signed not only by leading leave campaigners Daniel Hannan, Gisela Stuart and Douglas Carswell but also by remainers such as Cooper and the TUC general secretary, Frances O’Grady, urged all politicians to give an unequivocal commitment to protect the status of EU nationals.

They say this is not only necessary to put the UK in a strong position to seek protection for Britons in other EU countries, but it will also “send a clear statement to the extreme minority – who appear to believe they have licence to attack and harass migrants – that the British public finds their views repugnant and unwelcome in our society”.

The precise legal status of EU citizens in Britain is unclear and it is often assumed they will have individual “acquired rights” under the 1969 Vienna convention, including the right to live, work and retire in a country.

But Sionaidh Douglas-Scott, professor of law at Queen Mary University of London, and an expert in European law, has said: “There is no cast-iron guarantee on acquired rights in the event Britain leaves the EU. If you leave the EU you are no longer a member of the club that gives you those rights.”

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Other legal experts, including Nick Rollason of the law firm Kingsley Napley, believe that when the key moment comes it will be necessary to be able to prove that an EU national has the right to remain and work in Britain. “It won’t be enough just to show your passport,” he said.

One way of doing this might be to spend £65 on a Home Office permanent resident’s card certifying that the holder enjoys the right to live and work in Britain.

Others are also concerned for the future fate of those who are not lawfully in Britain. Saira Grant of the Joint Council for the Welfare of Immigrants has said that “those who are without status in our country who live in fear must now be given rights”. Boris Johnson held out the possibility of an amnesty for those who had lived in Britain without lawful status for 12 years or more. But their amnesty hopes probably died along with the implosion last Thursday of his Tory leadership bid.